Universal Relations and #P-Completeness

  • Hervé Fournier
  • Guillaume Malod
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3998)


This paper follows the methodology introduced by Agrawal and Biswas in [AB92], based on a notion of universality for the relations associated with NP-complete problems. The purpose was to study NP-complete problems by examining the effects of reductions on the solution sets of the associated witnessing relations. This provided a useful criterion for NP-completeness while suggesting structural similarities between natural NP-complete problems. We extend these ideas to the class #P. The notion we find also yields a practical criterion for #P-completeness, as illustrated by a varied set of examples, and strengthens the argument for structural homogeneity of natural complete problems.


Candidate Solution Hamiltonian Cycle Hamiltonian Path Satisfying Assignment Universal Relation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hervé Fournier
    • 1
  • Guillaume Malod
    • 2
  1. 1.Laboratoire PRiSMUniversité de VersaillesSt-Quentin en YvelinesFrance
  2. 2.Laboratory of Prof. Masahiko SATO, Graduate School of InformaticsKyoto UniversityJapan

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